Towards Safe Learning-Based Non-Linear Model Predictive Control through Recurrent Neural Network Modeling

Abstract

The practical deployment of nonlinear model predictive control (NMPC) is often limited by online computation: solving a nonlinear program at high control rates can be expensive on embedded hardware, especially when models are complex or horizons are long. Learning-based NMPC approximations shift this computation offline but typically demand large expert datasets and costly training. We propose Sequential-AMPC, a sequential neural policy that generates MPC candidate control sequences by sharing parameters across the prediction horizon. For deployment, we wrap the policy in a safety-augmented online evaluation and fallback mechanism, yielding Safe Sequential-AMPC. Compared to a naive feedforward policy baseline across several benchmarks, Sequential-AMPC requires substantially fewer expert MPC rollouts and yields candidate sequences with higher feasibility rates and improved closed-loop safety. On high-dimensional systems, it also exhibits better learning dynamics and performance in fewer epochs while maintaining stable validation improvement where the feedforward baseline can stagnate.

Figures (3)

• Figure 1: Proposed Sequential Approximate MPC (Seq-AMPC) generates the horizon recursively with a shared simple RNN cell (hidden size 256) and output head, preserving the same final output format $\hat{U}_t\in\mathbb{R}^{N \times n_u}$. Seq-AMPC replaces $\Pi_{\text{AMPC}}$ of hose_approximate_2025, resulting in a better-aligned controller, particularly in producing feasible horizon proposals. For deployment, Seq-AMPC is embedded in a safety-augmented online evaluation and fallback wrapper: candidate sequences are checked for feasibility and cost, and, if necessary, a safe fallback candidate and terminal controller are applied. We refer to the overall wrapped controller as Safe Seq-AMPC.
• Figure 2: Learning curves of AMPC (MLP) and Seq-AMPC (RNN) on the single-track vehicle model tasks, for the kinematic model on the left and the dynamic model on the right. Seq-AMPCs converged to lower validation losses. Early stopping was used to avoid overfitting to the training datasets.
• Figure 3: Examples of a naive and a safe trajectory are shown. Two blue-colored blocks are the obstacles that the vehicle needs to avoid. The non-safe trajectory collides at the red cross while the safe trajectory is able to reach and stop at the target point without collision.